Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 |
Z wnętrza książki
Wyniki 1 - 5 z 14
Strona 31
... angle , so is the co- sine of the adjacent leg to the co - sine of the ... vertical angles : For since radius : sine BCA : : co - sine CB : co - sine A ... angle at the base to the tangent of the perpendicular . For , supposing CEF as ...
... angle , so is the co- sine of the adjacent leg to the co - sine of the ... vertical angles : For since radius : sine BCA : : co - sine CB : co - sine A ... angle at the base to the tangent of the perpendicular . For , supposing CEF as ...
Strona 35
... angles at the base is to the tangent of half their difference , so is the tangent of half the vertical angle to the tangent of the angle which the perpen- dicular CD makes with the line CF bisecting the vertical angle . DEMONSTRATION ...
... angles at the base is to the tangent of half their difference , so is the tangent of half the vertical angle to the tangent of the angle which the perpen- dicular CD makes with the line CF bisecting the vertical angle . DEMONSTRATION ...
Strona 42
... angles A , B , pose AC As co - tang . : tang . 2 ABC - A 2 12 and ACB ACB :: tang . : tang . of the angle inclu- 2 ded by the perpendicular and a line bi- secting the vertical angle ; whence ACD is also known ; then ( by Theor . 5 ...
... angles A , B , pose AC As co - tang . : tang . 2 ABC - A 2 12 and ACB ACB :: tang . : tang . of the angle inclu- 2 ded by the perpendicular and a line bi- secting the vertical angle ; whence ACD is also known ; then ( by Theor . 5 ...
Strona 66
... vertical angle to the co - sine of half the difference of the angles at the base . In AC , produced , take CD = CB ; join B , D , and draw CE parallel to AB , and CF perpendicular to BD . Since CD CB , therefore is the angle D = DBC ...
... vertical angle to the co - sine of half the difference of the angles at the base . In AC , produced , take CD = CB ; join B , D , and draw CE parallel to AB , and CF perpendicular to BD . Since CD CB , therefore is the angle D = DBC ...
Strona 67
... to the difference of the segments of the base ( fig . 25. ) , so is the co- sine of half the vertical angle to the sine of half the difference of the angles at the base . For AC + BC : AQ - BQ :: AB PLANE TRIANGLES . 67.
... to the difference of the segments of the base ( fig . 25. ) , so is the co- sine of half the vertical angle to the sine of half the difference of the angles at the base . For AC + BC : AQ - BQ :: AB PLANE TRIANGLES . 67.
Inne wydania - Wyświetl wszystko
Kluczowe wyrazy i wyrażenia
ABDP AC by Theor adjacent angle arch bisecting chord circle passing co-sine AC co-tangent of half common logarithm common section Comp describe the circle E. D. COROLLARY E. D. PROP equal to half extremes gent given angle given circle given point half the difference half the sum half the vertical Hence hyperbolic logarithm hypothenuse inclination intersect leg BC line of measures original circle parallel perpendicular plane of projection plane triangle ABC primitive PROB produced projected circle projected pole projecting point radius rectangle right line right-angled spherical triangle SCHOLIUM secant semi-tangents sides similar triangles sine 59 sine AC sine of half sphere spherical angle SPHERICAL PROJECTIONS spherical triangle ABC sum or difference tangent of half THEOREM THOMAS SIMPSON triangle ABC fig versed sine vertical angle whence
Popularne fragmenty
Strona 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Strona 79 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...
Strona 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Strona 28 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.
Strona 7 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those...
Strona 28 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.